The bug
Pressing and holding down E (or whatever custom key binding) causes the inventory to flicker independent of if this starts while the inventory is open or closed. Pressing and holding down ESC will pause the game if and stay in the pause menu. Pressing and holding down ESC while in the pause menu, will first unpause the game and then pause it again, where it will stay.
This seems like inconsistent handling of the key down events.
I have not figured out when this behavior was introduced, but in far older versions (e.g. Beta 1.6.6), I noticed that these keys only open or closed the corresponding menu once.

Expected behavior:
The inventory would only open or closes once and the pause menu would only to open or closes once too.